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RJ131  Rfi9^64081222 

ttJlJl  057  The  growth  of  childr 


RECAP 


COMPLIMENTS    OF   THE    WRITER. 


THE  GROWTH  OF  CHILDREN, 


SrXTDIED    BY 


GALTON'S  METHOD  OF  PERCENTILE  GRADES, 


By  H.  p.  BOWDITCH,  M.D., 

TROFESSOK   OF   PHTSIOLOGY,   HARVARD   MEDICAL   SCHOOL. 


Reprinted  from  the  Twenty-second  Annual  Report  of  the  State  Board  of  Health  of  Massachusetts. 


K113- 


J^in7 


CoHege  of  ^Jpsicians  anh  burgeons 
ILihvarp 


Digitized  by  the  Internet  Archive 

in  2010  with  funding  from 

Open  Knowledge  Commons 


http://www.archive.org/details/growthofchildrenOObowd 


THE  GROWTH  OF  CHILDREN, 


STUDIED    BY 


GALTON'S  METHOD  OF  PEECENTILE  GEADES, 

By  H.  p.  BOWDITCH,  M.D., 

PEOrESSOE  OF  PHTSIOLOGT,  HAEVAED   MEDICAL   SCHOOL. 


Reprinted  from  the  Twenty-second  Annual  Report  of  the  State  Board  of  Health  of 
Massachusetts.    Boston,  1891. 


THE  GEOWTH  OF  CHILDEEN, 


STUDIED    BT 


GALTON'S   METHOD   OF  PERCENTILE   GRADES, 
By  H.  p.  Bowditch,  M.D., 

Professor  of  Physiology,  Harvard,  Medical  School. 


In  the  last  report  of  the  Massachusetts  State  Board  of 
Health  the  advantages  of  discussing  statistical  data  by  Gal- 
ton's  method  *  of  percentile  grades  were  explained  and  illus- 
trated in  a  paper  entitled  "  The  Physique  of  Women  in 
Massachusetts."  The  value  of  the  method  in  anthropomet- 
rical  work  seemed  so  obvious  that  it  has  been  thought  desir- 
able to  apply  it  to  the  large  body  of  observations  on  the 
height  and  weight  of  Boston  school  children  which  formed 
the  basis  of  an  article  on  "The  Growth  of  Children,"  pub- 
lished by  the  Board  of  Health  in  1877. 

In  this  article,  at  the  suggestion  of  Mr.  Charles  Roberts, 
tables  were  given  showing  the  distribution  of  the  observa- 
tions ;  i.e.,  the  number  of  individuals  at  each  age  whose 
height  was  recorded  at  each  successive  inch  or  whose  weight 
fell  within  successive  groups  of  four  pounds  each.  From 
these  tables  (tables  4  to  15  of  the  above-mentioned  article) 
it  was  easy  to  calculate  the  values  at  the  various  percentile 
grades.  For  example,  it  appears  from  Table  4  that  the 
heights  of  848  boys  between  five  and  six  years  old  were 
distributed  as  shown  in  the  following  table  :  — 

*  See  "  Galton,  Natural  Inheritance,"  London,  McMillan  &  Co.,  1889. 


480 


STATE  BOARD  OF  HEALTH.     [Pub.  Doc. 


Distribution  of  Observations  on  Heights  of  Boston  School-boys.    Age  at 
Last  Birthday  Five  Tears. 


Inches. 

jSTumber  of 
observations. 

Indies. 

Number  of 
observations. 

Inches. 

Number  of 
observations. 

47 
46 
45 
44 
43 
42 

4 

S 

20 

62 

119 

149 

41 
40 
39 
3S 
37 
36 

190 

149 

79 

42 

17 

7 

35 
34 
33 
32 
31 
30 

1 
1 

Total  number  of  observations, 


In  this  table  it  will  be  seen  that  five  percent.,  for  instance, 
of  the  total  number  of  observations  is  42.4.  Now  since  the 
observations  corresponding  to  each  successive  inch  include 
all  the  measurements  between  that  inch  and  the  next  inch 
above,  it  is  evident  that  there  are  l  +  l-}-7-|-17  =  26  individ- 
uals less  than  38  inches  in  height  and  l-|-l  +  7-{-17+42  =68 
individuals  less  than  39  inches  in  height.  Since,  therefore, 
42.4  lies  between  26  and  68  it  follows  that  the  height  below 
which  five  per  cent,  of  the  observations  fall  must  be  between 
38  and  39  inches.  The  exact  height  can  readily  be  calcu- 
lated by  interpolation.  Thus  the  fraction  of  an  inch  to  be 
added  to  38  to  give  the  required  height  is  obtained  by  dividing 
16.4  {i.e.,  42.4  —  26)  by  42  {i.e.,  the  number  of  observa- 
tions between  38  and  39  inches).  This  fraction  is  0.39,  and, 
therefore,  38.39  inches  is  the  height  below  which  five  per 
cent,  and  above  which  ninety-five  per  cent,  of  the  observa- 
tions fall ;  i.e.,  it  is  the  value  of  the  five  per  cent,  grade. 

In  this  way  tables  1  to  12  have  been  calculated  from  tables 
4  to  15  inclusive  of  the  original  article.  These  tables  show 
the  heights  and  weights  of  Boston  school  children  of  both 
sexes  and  various  ages  at  percentile  grades  varying  from  five 
per  cent,  to  ninety-five  per  cent.  Separate  tables  are,  more- 
over, given  for  children  of  American  parentage,  Irish  parent- 
age, and  for  the  whole  number  of  observations  irrespective  of 
nationality.  The  values  are  given  in  both  the  English  and 
the  metric  system  of  weights  and  measures,  and  in  the  last 


No.  34.]      THE  GROWTH  OF  CHILDEEN.  481 

column  of  each  table  are  to  be  found  the  average  heights 
and  weights  of  children  of  each  age  as  given  in  the  original 
article. 

The  conclusions  which  may  be  drawn  from  a  study  of  these 
tables  will  be  best  understood  after  an  examination  of  the 
curves  which  have  been  constructed  from  them,  and  as  a 
preliminary  to  this  study  it  will  be  well  to  consider  briefly 
the  general  character  of  curves  representing  values  at  various 
percentile  grades. 


482 


STATE  BOARD   OF  HEALTH. 


[Pub.  Doc. 


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485 


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487 


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494 


STATE  BOAED   OF  HEALTH.      [Pub.  Doc. 


A  geometrical  construction  of  a  special  case  will  perhaps 
best  serve  to  place  the  matter  in  a  clear  light.  Let  us  sup- 
pose one  thousand  grown  men  standing  in  line  arranged 
according  to  height.  The  heads  of  these  men  will  form  a 
curved  line  represented  in  its  general  form  by  the  curve  ST 
in  Fig  1.    In  this  diagram  the  line  SO  represents  the  height 


Fig-.  1. 


Q      5%  I  OX       20;^       307      40%      50%      60%      70%       80%      90X  Q5°A  Q' 


of  the  shortest  and  the  line  TO^  that  of  the  tallest  man.  The 
curve  ST,  representing  the  heights  of  the  intermediate  men, 
is  approximately  a  straight  line  in  a  large  part  of  its  course 
fcut  bends  up  sharply  at  the  right  and  down  sharply  at  the 
left  owing  to  the  presence  of  a  few  very  tall  and  a  few  very 
short  men.  Mediocrity  is  the  rule  and  extremes  the  excep- 
tion in  height  as  in  everything  else. 

If  now  we  divide  this  row  of  men  into  two  equal  parts 
and  ascertain  tbe  height  of  the  five  hundredth  man  in  the 
row  (or,  more  accurately  speaking,  the  height  half  way 
between  that  of  the  five  hundredth  and  that  of  the  five 
hundred  and  first  man)  we  shall  have  a  value  below  which 
one  half  and  above  which  the  other  half  of  the  observations 
lie.  This  value  is  termed  by  Galton  the  value  of  the  fifty 
percentile  grade,  or  the  median  value,  and  is  designated  by 


No.  34.]      THE  GROWTH  OF  CHILDEEN. 


495 


the  letter  M.  In  the  same  way  the  values  at  other  percen- 
tile grades  may  be  determined  by  dividing  the  row  at  points 
corresponding  to  various  percentages  of  the  total  number  of 
observations.  The  percentile  grades  indicated  in  Fig.  1  are 
those  adopted  by  Galton,  and  are  practically  sufficient  to 
indicate  the  character  of  the  curve.  With  a  very  large 
number  of  observations  it  would  of  course  be  possible  to 
determine  values  below  five  per  cent,  and  above  ninety-five 
percent.,  but  in  anthropometrical  investigations  with  existing 
data  it  does  not  seem  wise  to  go  beyond  these  limits. 

It  is  evident  that  the  value  M  will  tend  to  approximate  to 
the  average  value  of  all  the  observations  and  will  be  identical 
with  it  when  the  curve  ST  is  symmetrically  disposed  on  both 
sides  of  M,  i.e.,  when  the  values  at  sixty,  seventy,  eighty, 
ninety  and  ninety-five  per  cent,  exceed  M  by  the  same  amount, 
respectively,  by  which  the  values  at  forty,  thirty,  twenty, 
ten  and  five  per  cent,  fall  short  of  it.  If  A  represent  the 
average  value  of  all  the  observations,  then  the  value  of  M — A 
will  be  a  measure  of  the  direction  and  extent  of  the  asym- 
metry of  the  curve  ST,  for  this  value  will  be  zero  when  the 
curve  is  symmetrical,  positive  when  the  values  at  the  lower 
percentile  grades  fall  short  of  M  more  than  those  at  the  higher 
grades  exceed  it,  and  negative  when  the  reverse  is  the  case. 

Let  us  now  apply  this  test  to  the  data  in  our  possession, 
confining  our  attention  for  the  present  to  tables  1,  4,  7  and 
10,  which  give  the  total  number  of  observations  irrespective 
of  nationality.  By  subtracting  the  average  from  the  median 
values  in  these  four  tables  the  following  table  (No.  12a)  has 
been  constructed  :  — 


Table  12a,  —  Values  of  M—A. 


Age  at  Last  Birthday. 


Five,    . 

Six,      . 

Seven, . 

Eight,  . 

Nine,    . 

Ten,     , 

Eleven, 

Twelve, 

Thirteen, 

Fourteen, 

Fifteen, 

Sixteen, 

Seventeen, 

Eighteen, 


Heights  in  Inches. 


Boys. 


+0.10 
4-0.12 
-1-0.09 
-1-0.08 
-i-0.08 
-1-0.05 
-1-0.  OT 
0.00 
—0.2.3 
—0.28 
-1-0.07 
+0.35 
-1-0.05 
-1-0.13 


--0.14 
--0.05 
--0.11 
--U.OT 
--0.17 
+0.12 
—0.01 
0.00 
+0.24 
+0.26 
4-0.11 
4-0.19 
-1-0.26 
—0.10 


Weights  in  Podnds. 


Boys. 


—0.13 

—0.03 

—0.15 

—0.17 

— O.IT 

—0.16 

—0.35 

—0.59 

—0.28 

—0.45 

—0.12 

—0.95 

—0.44 

—1.22 

—1.18 

—1.23 

—1.94 

—0.63 

— 1.S8 

—0.68 

—1.10 

—0.97 

+0.37 

—0.76 

—0.92 

—2.77 

—0.84 

—2.52 

496 


STATE  BOARD  OF  HEALTH.     [PuId.  Doc. 


An  examination  of  this  table  or  of  the  curves  constructed 
from  it,  as  given  in  Plate  1,  shows  that  the  asymmetry  of 


PLATE  I. 

HEIGHTS  OF  BOSTON  SCHOOL  CHILDREN 
•n  MEDIAN    MINUS  AVERAGE  VALUES  (M-A) 


0.4 


0.2 


0.2 


0.4- 


2.0 


3.0 


AGE     AT     LAST     BIRTHDAY 
5        6         7         8        9        10        H        12       13        14       15       t6      U        18 


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GIRL 

WEIGHTS  OF  BOSTON  SCHOOL  CHILDREM, 

MEDIAN  MINUS  AVERAGE  VALUES  (M-A) 

AGE    AT   LAST    BIRTHDAY 
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No.  34.]      THE   GROWTH  OF  CHILDREN.  497 

the  curves  of  percentile  grades  varies  very  much,  at  different 
ages,  both  in  direction  and  amount.  The  variation  in  the 
value  of  M — A  in  the  curves  of  height  is  much  the  same  as 
that  in  the  curves  of  weight  for  each  sex  considered  by  itself, 
but  there  is  a  great  difference  between  the  two  sexes.  This 
difference  shows  itself  most  distinctly  between  the  ages  of 
eleven  and  fifteen  years.  During  this  time  a  rise  in  the 
curves  for  the  males  coincides  with  a  fall  in  those  for  the 
females,  while  before  and  after  this  period  the  curves,  as  a 
rule,  rise  and  fall  together.  We  must  conclude,  therefore, 
that  the  rate  of  annual  increase  both  in  height  and  weight  is 
different  at  different  percentile  grades,  or,  in  other  words, 
that  large  children  grow  differently  from  small  ones,  and 
moreover,  that  between  the  ages  of  eleven  and  fifteen  years 
there  is  a  striking  difference  in  the  mode  of  growth  of  the 
two  sexes.  The  significance  of  this  conclusion  will  be  made 
clearer  by  an  examination  of  the  curves  constructed  directly 
from  the  tables  of  percentile  grades.  Curves  of  this  sort  are 
presented  in  plates  2,  3,  4  and  5,  constructed  from  tables  1, 
4,  7  and  10,  containing  the  total  number  ot  observations  irre- 
spective of  nationality.  Similar  curves  have  been  obtained 
from  the  remaining  tables  in  which  the  observations  are 
grouped  according  to  the  nationality  of  the  parents,  but  as 
they  are  less  regular,  owing  to  the  smaller  number  of  obser- 
vations from  which  they  are  constructed,  and  lead  to  no 
additional  conclusions,  it 'has  not  been  thought  worth  while 
to  present  them. 

A  glance  at  the  curves  on  plates  2-5  shows  at  once  the 
nature  of  the  asj^mmetry,  the  existence  of  which  is  indicated 
by  the  curves  on  Plate  1.  It  will  be  observed  that  during  the 
earlier  years  of  school  life  the  curves  for  the  successive  years 
are  fairly  symmetrical,  which  is  in  harmony  with  the  previous 
observation  that  in  these  years  the  value  of  M — A  does  not 
differ  widely  from  zero.  At  about  ten  years  of  age  in  girls 
and  eleven  or  twelve  years  in  boys,  the  curves  become  dis- 
tinctly asymmetrical,  owing  to  the  values  increasing  more 
rapidly  at  the  higher  than  at  the  lower  percentile  grades. 
At  the  age  of  twelve  or  thirteen  years  in  girls  and  fourteen 
or  fifteen  years  in  boys  an  asymmetry  in  the  opposite  direc- 
tion shows  itself,  since  at  this  period  the  values  are  increasing 


498 


STATE  BOARD  OF  HEALTH.  [Pub.  Doc. 


PLATE  2.  (from  table  I.) 

HEIGHTS  OF  BOSTON  SCHOOLBOYS, 
IRRESPECTIVE  OF  NATIONALITY. 


HEIGHT 
INCHES. 

'72 

70 
'68 

66 

64 

62 

60 

58 

56 

54- 

52 

50 

48 

46 

44 

42 

40 

38 


10 


PERCENTILE     GRADES. 
20  30  40  50  60  70 


80 


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AGE 
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No.  34.] 


THE  GROWTH  OF  CHILDREN. 


499 


PLATE  3. (from  table  4..) 

WEIGHTS  OF   BOSTON  SCHOOLBOYS. 
IRRESPECTIVE  OF  NATIONALITY. 


20 


PERCENT!  LE  G  RADES. 
30  40  50  60  70 


80 


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YR5 


500 


STATE  BOARD  OF  HEALTH.  [Pub.  Doc, 


PLATE  4.  (from  table  7  ) 

HEIGHTS    OF  BOSTON  SCHOOLGIRLS. 
IRRESPECTIVE  OF  NATIONALITY. 


KE(GHT 
INCHES.     (0 


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No.  34.1 


THE  GROWTH  OF  CHILDREN. 


501 


PLATE  5.  (prom  table  10.) 

WEIGHTS  OF  BOSTON  5CH00LGIRL5.- 
IRRESPECTIVE  OF  NATIONALITY. 


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502  STATE  BOAKD  OF  HEALTH.     [Pub.  Docv. 

more  rapidly  at  the  lower  than  at  the  higher  percentile  grades. 
These  changes  correspond  accurately  with  the  fall  and  rise  in 
the  value  of  M — A,  as  shown  on  Plate  1. 

In  the  original  article  on  the  growth  of  children  it  was 
shown  that  about  two  years  before  the  age  of  puberty  there 
is  a  period  during  which  the  growth  in  both  height  and 
weight  shows  a  distinct  acceleration.  Now,  the  rate  of  growth 
at  the  various  percentile  grades  is  represented  on  plates  2-5 
by  the  vertical  distances  between  the  curves  corresponding  to 
the  successive  years  ;  and  an  inspection  of  these  curves  shows 
that  the  prepubertal  period  of  accelerated  growth,  already 
shown  to  exist  by  a  comparison  of  average  heights  and 
weights  at  different  ages,  occurs  all  along  the  line,  but  that 
it  occurs  earlier  at  the  higher  than  at  the  lower  percentile 
grades.  In  other  words,  we  find  that  the  above-mentioned 
variations  in  the  value  of  M — A  are  due  to  the  fact  that  the 
period  of  acceleration,  which  is  such  a  distinct  phenomenon 
in  the  growth  of  children,  occurs  at  an  earlier  age  in  large 
than  in  small  children. 

The  significance  of  this  observation  will  be  best  understood 
by  an  examination  of  the  annual  increase  in  height  and 
weight  of  children  at  the  different  percentile  grades.  These 
values,  which  are  readily  obtained  from  the  preceding  tables 
by  subtracting  the  height  or  weight  at  any  year  from  that  of 
the  year  next  following,  are  shown  in  tables  13,  14,  15  and 
16,  which  have  been  calculated  from  tables  1,  4,  7  and  10 
respectively.* 


*  It  will  be  noticed  that  in  tables  1, 4,  7  and  10  the  ages  are  given  "  at  the  last  birth- 
day." Hence  the  average  age  of  the  children  thus  grouped  together  will  be  six  months 
greater  than  the  age  given  in  the  tables.  For  instance,  in  Table  1,  five  years  six 
months  is  the  average  age  of  the  848  boys  whose  heights  at  various  percentile  grades 
are  given  in  the  first  line.  Now  since  the  figures  in  the  tables  of  annual  increase  are 
the  differences  between  the  successive  heights  and  weights  in  tables  1,  4,  7  and  10,  it 
is  evident  that  they  express  the  yearly  growth  precisely  at  the  age  given  in  the  tables. 
The  first  line  in  Table  13,  for  instance,  is  the  annual  growth  in  height  of  boys  of  six 
years  of  age. 


No.  34.]      THE  GROWTH  OF  CHILDREN. 


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No.  34.]  THE   GROWTH  OF  CHILDREN. 


507 


The  conclusions  to  be  drawn  from  these  tables  will  be  most 
readily  understood  by  an  examination  of  the  curves  on  plates 
6  and  7,   which   have  been  constructed  from  them,   the  curves 


GIRLS 


PLATE  6.(pRO'^  TABLES  13  8c  15.)    BOYS  — 

ANNUAL   INCREASE   IN   INCHES 

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STATE  BOARD  OF  HEALTH.        [Pub.  Doc. 


representing  the  yearly  growth  of  the  two  sexes  being,  for  easier 
comparison,  plotted  on  the  same  system  of  co-ordinates. 


PLATE   7  (F POM  TABLES  14. ft  16)  BOYS- 


GIRLS' 


ANNUAL  INCREASE  IN  POUNDS. 

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95%  6 


No.  34.]       THE  GROWTH  OF  CHILDREN.  509 

The  followino^  are  the  most  obvious  conclusions  :  — 

1.  The  maximum  yearly  growth  in  both  height  and  weight 
is  at  all  percentile  grades  greater  in  boys  than  in  girls,  and 
occurs  in  boys  two  or  three  years  later  than  in  girls. 

2.  The  age  at  which  this  maximum  yearly  growth  in 
height  and  weight  is  reached  is,  in  both  sexes,  earlier  at  the 
higher  than  at  the  lower  percentile  grades,  the  range  being 
from  twelve  to  fourteen  years  for  girls  and  from  fourteen  to 
sixteen  years  for  boys.  In  other  words,  large  children  make 
their  most  rapid  growth  at  an  earlier  age  than  small  ones. 

3.  The  curves  representing  the  annual  growth  of  boys 
are  characterized  on  either  side  of  the  maximum  by  a  steeper 
rise  and  fall  in  the  lower  than  in  the  higher  percentile  grades, 
though  the  maximum  itself  may  be  quite  as  high  in  the  former 
as  in  the  latter  grades.  This  indicates  that  the  above-men- 
tioned period  of  accelerated  growth  in  large  boys  differs 
from  that  in  small  boys  rather  in  duration  than  in  intensity. 
In  girls  a  difference  of  this  sort  does  not  seem  to  exist. 

4.  In  boys  at  eleven  years  of  age  there  is  a  period  of 
remarkably  slow  growth  both  in  height  and  weight,  the  curves 
of  annual  increase  in  nearly  all  the  percentile  grades  reach- 
ing at  this  age  a  lower  point  than  for  several  years  preceding 
or  subsequent  to  this  age.  In  girls  a  similar  but  less  marked 
period  of  retarded  growth  in  height  is  to  be  noticed  at  nine 
years  of  age,  but  the  rate  of  growth  in  weight  does  not  seem 
to  suffer  a  corresponding  diminution.* 

One  of  the  conclusions  reached  in  the  original  article  to 
which  reference  has  been  made  was  that  "  at  about  thirteen 
or  fourteen  years  girls  in  this  community  are,  during  more 
than  two  years,  both  taller  and  heavier  than  boys  at  the  same 
age,  though  before  and  after  that  period  the  reverse  is  the 


*  It  is  interesting,  however,  to  notice  that  in  the  curves  constructed  by  Dr. 
Stevenson  (See  "  Lancet,"  Sept.  22,  1888)  from  English  and  American  statistics,  and 
representing  the  annual  Increase  in  weight  of  "  hoys  and  girls  of  the  English-speaking 
races,"  the  period  of  retarded  growth  is  a  marked  phenomenon  in  both  sexes,  occur- 
ring in  boys  at  eleven  and  in  girls  at  nine  years  of  age. 

See  also  "  Axel  Key,  Die.  Pubertiltsentwickelung."  (Verhandlungen  des  X  inter- 
nationalen  medicinschen  Congresses,  Berlin,  1890.  Bd.  1.,  p.  67  )  This  observer 
finds  that  in  Sweden  the  period  of  least  increase  in  height  and  weight  occurs  at  ten 
years  for  boys  and  nine  years  for  girls. 


510  STATE  BOARD   OF  HEALTH.      [Pub.  Doc. 

case."  The  dependence  of  this  phenomenon  upon  the  fact 
that  the  prepubertal  period  of  accelerated  growth  occurs 
earlier  in  girls  than  in  boys  was  also  pointed  out.  It  will  be 
interesting  now  to  inquire  in  what  way  this  period  of  female 
superiority  is  ajffected  by  the  fact  that  the  maximum  rate  of 
growth  is  reached  earlier  in  the  higher  than  in  the  lower 
percentile  grades.  The  influence  of  this  circumstance  is 
readily  understood  from  an  inspection  of  the  curves  on 
plates  8  and  9,  which  have  been  constructed  from  the  fig- 
ures on  plates  1,  4,  7  and  10.  Here  the  absolute  heights  and 
weights  of  boys  and  girls  of  the  same  percentile  grade  are 
plotted  on  the  same  system  of  co-ordinates,  while  the  ordi- 
nates  for  the  successive  percentile  grades  difier  from  each 
other  by  five  inches  or  twenty-five  pounds  respectively. 

In  this  way  the  curves  are  brought  vertically  over  one 
another  and  a  comparison  between  them  is  facilitated.  The 
points  where  the  curves  of  growth  of  the  two  sexes  intersect 
each  other  are  joined  by  dotted  lines,  in  order  that  the 
periods  of  female  superiority  at  the  various  percentile  grades 
may  be  readily  compared  with  each  other.  A  glance  at  the 
curves  suffices  to  show  that  the  period  of  female  superiorit}'^ 
is  to  be  observed  at  all  percentile  grades  both  in  height  and 
weight,  and,  moreover,  that  it  both  begins  and  ends  earlier  in 
the  higher  than  in  the  lower  percentile  grades.  Thus,  in  the 
ninety-five  percentile  grade,  girls  begin  to  exceed  boys  in 
height  at  the  age  of  ten  years  four  months  and  are  in  turn 
surpassed  by  them  at  thirteen  years,  while  in  the  five  per- 
centile grade  girls  do  not  surpass  boys  in  height  till  they 
are  eleven  years  five  months  old  and  boys  do  not  regain 
their  superiority  till  they  are  fifteen  years  four  months  of 
age.  It  will  be  also  noticed  that  the  duration  of  the  period 
of  female  superiority  varies  quite  regularly  with  the  percen- 
tile grade,  but  that  the  variations  in  height  and  weight  are 
in  opposite  directions.  This  is  indicated  by  the  fact  that 
the  above-mentioned  dotted  lines  converge  upward  in  the 
curves  of  height  and  downward  in  those  of  weight.  In 
other  words,  we  may  say  that,  when  growing  children  of 
both  sexes  are  compared  together  by  corresponding  percen- 
tile grades,  the  period  of  female  superiority  in  height  is  less 
conspicuous  in  tall  than  in  short  children,  while  the  period 


No.  34.]  THE   GROVYTH  OF  CHILDREN. 


511 


GIRLS- 


PLATE    8.  (from  tables  I  &z)   boys  — 

I  HEIGHTS   OF   BOSTON  SCHOOL  CHILDREN. 

gSYBS.   6YRS     7^R5     S^RS     9YRS.    I0YR5     ||YR5    12YRS.  |3YRS.    |4YRS    15YR5    |6YRS     jJYRS 


512 


STATE  BOARD  OF  HEALTH.  [Pub.  D 


oc. 


PLATE    9    (FROM  TABLES  4  &  10.)    BOYS GIRLS 

WEIGHTS    OF  BOSTON   SCHOOLCHILDREN 


S5TRS    6"''"^    7YRS.  Qrns.  QYRS    iqyrs.  hyrs.  |2yrs.  13YRS.  )4yrs.  |5yrs.  |5yrs.  17YR& 


No.  34.]      THE  GROWTH  OF  CHILDREN. 


513 


of  female  superiority  in  weight  is  a  more  marked  phenome- 
non in  heavy  than  in  light  children. 

Among  the  advantages  of  this  method  of  discussing  anthro- 
pometrical  results  may  be  mentioned  the  facility  which  it 
affords  for  comparing  the  rates  of  growth  of  children  of 
different  nationalities  by  determining  the  percentile  rank 
of  the  average  children  of  one  nationality  referred  to  those 
of  another  nationality  as  a  standard.  We  may  take,  for 
instance,  the  observations  of  Pagliani*  on  Italian  children, 
and  those  of  Erismann|  on  the  employees  in  Russian  fac- 
tories, and  calculate  the  percentile  rank  of  the  children  at 
successive  ag-es  when  referred  to  Boston  children  as  a 
standard.  The  result  of  this  calculation  is  given  in  the 
followinof  table  :  — 


Table  17.  —  Shoiuing  the 
clren  compared  w 


Percentile  Rank  of  Italian  and  Eussian  CMl- 
ith  those  of  the  Boston  Public  Schools. 


Age  at  Last  Birthday. 


Five, 

Six, 

Seven,   . 

Eight,    . 

TSTine, 

Ten, 

Eleven, 

Twelve, 

Thirteen, 

Fourteen, 

Fifteen, 

Sixteen, 

Seventeen, 

Eighteen, 


Percentile  Rank. 


Italian  (Pagliani). 


Boys. 


below  5 
5.6 
22.1 
26.. T 
31.4 
20.0 
16.4 
16.1 
21.7 
21.2 
23.7 
16.2 
13.1 
6.6 


Girls. 


below  5 
below  5 

9.2 
15. S 
29.1 
28.0 
25.5 
24.1 
23.7 
30.0 
29.5 
32.4 
32.2 
34.3 


Eussian  (Erismann). 


Boys. 


75.9 

80.7 

56.6 

63.4 

48.9 

76.4 

40.6 

51.9 

42.5 

48.8 

36.6 

39.0 

28.7 

26.9 

26.5 

22.8 

29.1 

21.4 

17.7 

23.4 

18.6 

22.0 

15.0 

23.6 

An  examination  of  this  table  shows  that  Italian  children  of 
both  sexes  are,  in  early  life,  very  much  smaller  than  Boston 


*  Lo  Sviluppo  Umano,  p.  37. 

t  Untersuchungen  iiber  die  kOrperliche  Entwickelung  der  Fabrikarbeiter  in  Zen- 
tmlrussland,  Tiibingen,  1889.  A  very  thorough  investigation  based  upon  measure- 
ments of  over  100,000  individuals. 


514  STATE  BOARD  OF  HEALTH.     [Pub.  Doc. 

children  of  the  same  age,  and,  though  they  afterwards  increase 
in  relative  size,  they  never  reach  a  higher  percentile  than  31.4 
for  boys  and  32.4  for  girls. 

The  Russian  children  show  in  general,  with  increasing  age, 
a  progressive  diminution  in  percentile  rank  which  is  probably 
to  be  accounted  for  by  the  fact  that  during  the  earlier  period 
of  life  only  children  who  are  unusually  well  developed 
physically  are  likely  to  find  their  way  into  manufactories. 
The  children  from  seven  to  twelve  years  of  age  are  therefore 
to  some  extent  selected  cases  and  do  not  represent  the  aver- 
age development  of  the  working  population. 

It  will  be  noticed  that  throughout  this  article  it  has  been 
assumed  that  the  changes  from  year  to  year  in  the  values  of 
the  height  and  weight  at  the  various  percentile  grades  repre- 
sent the  rate  of  growth  of  large,  small  and  medium-sized 
children  respectively.  This  assumption  may  be  criticized  on 
the  ground  that  the  values  at  the  various  percentile  grades 
do  not  represent  the  average  measurements  of  particular 
groups  of  growing  children  but  are  merely  limiting  values, 
on  either  side  of  which  lie  certain  percentages  of  the  total 
number  of  observations  on  children  of  a  certain  age.  To 
determine  how  much  importance  is  to  be  attached  to  this 
objection  it  will  be  necessary  to  inquire  within  what  limits 
the  percentile  rank  of  a  growing  child  may  under  normal 
circumstances  vary  from  year  to  year,  for  it  is  obvious  that 
if  growing  children  remain  practically  in  the  same  percentile' 
grade  during  the  whole  period  of  adolescence  a  comparison 
of  the  values  at  the  various  percentile  grades  in  successive 
years  will,  to  all  intents  and  purposes,  show  the  annual 
increase  in  height  and  weight  of  groups  of  children  belonging 
in  and  about  those  percentile  grades,  i.e.,  it  will  really  give 
us  the  rate  of  growth  of  large,  small  and  medium-sized 
children.  Now  it  is  evident  that  a  close  maintenance  of  a 
given  percentile  rank  by  a  growing  child  is  by  no  means  a 
universal  rule,  for  it  is  a  matter  of  common  observation  that 
very  small  babies  sometimes  grow  up  into  very  large  men 
and  women.  Such  cases,  however,  always  attract  attention 
from  their  obviously  exceptional  character  and  indicate  that, 
as  a  rule,  there  is  a  certain  degree  of  correspondence  between 
the  size  of  the  child  and  that  of  the  adult. 


No.  34.]      THE  GROWTH  OF  CHILDREN.  515 

General  impressions  with  regard  to  such  questions  are,  of 
course,  of  very  little  value,  and  before  any  definite  conclu- 
sion can  be  reached  it  will  be  necessary  to  collect  large 
numbers  of  observations  on  growing  children  of  both  sexes, 
each  individual  being  measured  in  successive  years  or,  still 
better,  several  times  each  year,  and  the  percentile  rank  at 
each  age  determined.  Such  determinations  maybe  made  by 
means  of  tables  1-10,  or  by  the  curves  on  plates  2-5  con- 
structed from  them,  but  in  practice  it  will  be  found  more 
convenient  to  make  use  of  such  curves  as  those  on  plates 
10-13,  which  have  been  constructed  *  with  a  view  to  this 
special  purpose. 

In  these  plates,  which  have  been  constructed  only  from  the 
tables  which  present  the  total  number  of  observations  irre- 
spective of  nationality,  the  age  in  years  and  months  is  given 
on  the  sides,  the  percentile  rank  at  the  top  and  bottom,  while 
the  curved  lines  traversing  the  plate  represent  successive 
inches  or  pounds.  The  use  of  the  curves  will  be  best  under- 
stood by  an  example.  Let  us  suppose,  for  instance,  that  a 
boy  ten  years  five  months  old  measures  fifty  inches  in  height, 
and  it  is  desired  to  ascertain  his  percentile  rank.  On  Plate 
10  the  horizontal  line  corresponding  to  ten  years  five  months 
is  to  be  followed  to  its  point  of  intersection  with  the  fifty- 
inch  curve.  This  point  of  intersection  will  be  found  to  lie 
on  the  vertical  line  corresponding  to  twenty-five  per  cent. 
This  means  that  the  boy  is  taller  than  twenty-five  per  cent, 
and  shorter  than  seventy-five  per  cent,  of  the  boys  of  his 
age.  A  height  of  fifty-one  inches  at  the  same  age  would 
give  a  percentile  rank  of  forty-one  percent.,  fifty-two  inches 
fifty-seven  per  cent.,  fifty-three  inches  seventy-four  per 
cent.,  etc. 

If  we  were  in  possession  of  a  few  hundred  sets  of  observa- 
tions on  growing  children,  each  child  being  measured  and 
weighed  annually  or  semiannually  during  the  period  of 
adolescence    and    his    percentile    rank    determined  in  the 


*  Such  curves  may  be  constructed  by  calculating  for  each  age  the  percentile  rank 
corresponding  to  each  inch  or  pound  by  interpolation  in  tables  such  as  Nos.  1-12, 
or,  still  better,  from  tables  such  as  Nos.  4-15  of  the  original  article,  by  direct  ad- 
dition to  the  percentages  con*esponding  to  the  successive  inches  or  P9unds. 


516 


STATE  BOARD  OF  HEALTH.        [Pub.  Doc. 


PLATE    10 

SHOWING    PERCENTILE   RANK  OF  BOYS 
OF  GIVEN   AGE  AND  HEIGHT 


5'/.  107,         20%  30%        40°/         ?G%         60%         70%         60%      90%  95X 


5%  10%  20%         30%        .A0%  50%         60%         70%  80%       90%   957. 


No.  34.]  THE   GROWTH  OF  CHILDRE:^. 


517 


PLATE    I  I. 

SHOWING    PERCENTILE  RANK  OF  BOYS 
OF   GIVEN  AGE  AND  WEIGHT. 

5/.  10°/         207,        30%        40%         SOVo        60%        70%         80%        90%  957. 


AGE. 

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518  ^TATE  BOARD  OF  HEALTH.        [Pub.  Doc. 


PLATE    12. 

SHOWING  PERCENTILE  RANK  OF  GIRLS 
OF  GIVEN   AGE  AND  HEIGHT. 

5°/.  107         20%        30-/0        407.        50°/        60°/o        707o        607        90^/  957 

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No.  34.]  THE  GROWTH  OF  CHILDREN. 


519 


AGE 

YR5 

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PL'ATE    13 

SHOWING'   PERCENTILE    RANK    OF  GIRLS 
OF  GIVEN  A6E   AND  WEIGHT; 

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520 


STATE  BOARD   OF  HEALTH.     [Pub.  Doc. 


above  manner,  we  should  be  able  to  draw  fairly  accurate 
conclusions  as  to  the  normal  range  of  variation  in  percentile 
rank  during  the  period  of  growth,  and  to  determine  how  far 
the  rate  of  growth  in  the  earlier  years  of  life  is  to  be  regarded 
as  an  indication  of  the  size  to  be  subsequently  attained.  Un- 
fortunately records  of  this  sort  have  been  rarely  kept  and 
still  more  rarely  published.  Those  which  are  accessible  to 
the  writer  represent  in  most  cases  the  result  of  observations 
upon  children  above  the  ninety-five  per  cent,  grade  in  both 
height  and  weight,  i.e.,  of  a  size  at  which  the  above  tables 
do  not  permit  us  to  determine  the  percentile  rank  with  any 
accuracy.  As  an  example  of  the  kind  of  record  which  it  is 
important  to  secure  the  following  table  is  presented,  showing 
the  percentile  rank  in  height  and  weight  of  two  growing 
girls  from  the  ages  of  six  to  fifteen  years  :  — 

Table  18.  Shoiving  Absohite  Height  and  Weight  and  Percentile  Bank  in 
Height  and  Weight  of  tioo  Oirls  E  and  F  at  Various  Ages  from  Six  to 
Fifteen  Tears. 


These  records  are,  of  course,  not  numerous  enough  to 
justify  any  general  conclusions,  but  they  are  interesting  as 
showing  that  the  percentile  rank  of  healthy  growing  children 
may,  during  adolescence,  vary  within  a  range  of  four  or  five 


No.  34.]     THE  GROWTH  OF  CHILDREN.  521 

per  cent,  on  either  side  of  an  average  value.  How  much 
wider  the  variation  may  be  vvithout  passing  the  limits  of 
health  is  a  question  for  the  determination  of  which  a  very 
large  number  of  observations  is  necessary,  and  it  is  to  the 
public  schools  that  we  must  again  look  for  the  data  which 
shall  make  it  possible  to  give  a  definite  answer  to  this  and 
other  questions  relating  to  the  phenomena  of  growth.  Mean- 
while, the  above-described  variations  during  adolescence  of 
the  height  and  weight  of  children  at  the  various  percentile 
grades  must  be  regarded  as  representing  only  in  a  general  way 
the  rate  of  growth  of  large  and  small  children  respectively. 

The  importance  of  taking  periodical  measurements  of 
pupils  in  the  public  schools  has  frequently  been  urged.  In 
fact,  this  branch  of  anthropometry  stands  in  such  close  rela- 
tion to  physical  training  that  it  may  be  regarded  as  the 
test  to  which  systems  of  physical  training  must  be  subjected 
in  order  to  judge  of  their  comparative  efficiency.  No  teacher 
at  the  present  day  is  satisfied  to  give  instruction  in  any  de- 
partment of  learning  without  testing  its  results  by  periodical 
examinations  of  the  pupils.  In  the  same  way  the  director  of 
physical  training  can  have  no  certainty  that  his  efforts  are 
well  directed  unless  he  can  convince  himself,  by  periodical 
determinations  of  height,  weight,  chest  girth,  strength,  etc., 
that  his  pupils  are  making  satisfactory  progress  in  physical 
development. 

Here  the  question  at  once  arises  :  What  amount  of  prog- 
ress is  to  be  regarded  as  satisfactory  ?  and  the  importance 
of  establishing  a  normal  standard  of  development  becomes 
apparent.  A  rough  approximation  to  such  a  standard  of 
development  in  height  and  weight  for  the  pupils  of  the 
Boston  public  schools  has  been  given  in  the  above  tables  and 
curves.  By  their  means  it  is  possible  to  ascertain  whether 
a  given  pupil  retains  his  rank  (relative  to  height  and  weight) 
among  his  comrades  during  the  period  of  adolescence.  It 
is  obvious,  however,  that  much  more  valuable  results  could 
be  obtained  if  we  were  in  possession  of  observations  numer- 
ous enough  to  justify  the  construction  of  separate  tables  and 
curves  for  children  of  different  nationalities ;  for  it  has  been 
shown  that  children  of  American  parentage  in  our  public 


522        STATE  BOAKD  OF  HEALTH.     [P.  D.  No.  34.] 

schools  are,  at  nearly  all  ages,  taller  and  heavier  than  those  of 
other  nationalities.  It  is  also  of  great  importance  that  some 
simple  tests  of  strength  should  be  applied  to  growing  children 
in  order  to  establish  a  standard  of  power  as  well  as  of  size. 
When  a  system  of  annual  physical  measurements  shall  have 
been  introduced  into  our  public  schools  and  recognized  as  of 
equal  importance  with  the  annual  examinations  in  the  vari- 
ous studies,  we  shall  be  in  a  position  to  formulate  the  laws 
of  growth  with  much  greater  accuracy  than  is  at  present 
possible. 


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